Laser speckle velocimeter for a robotized vehicle

Transcription

1 Laser speckle velocimeter for a robotized vehicle A.A. Aliverdiev a, M.A. Caponero b, C. Moriconi c, P.A. Fichera c, and G. Sagratella c* a Institute of Physics, Daghestan Scientific Center of Russian Academy of the Sciences, Yaragskogo, 94, 3673, Makhachkala, Russia; b Applied Physics division, ENEA Frascati, V. E. Fermi 45, 44 Frascati, Italy; c Robotics and Informatics division, ENEA Casaccia, V. Anguillarese 31, 6, Roma, Italy; ABSTRACT The paper points out the progress in the exploitation of high, fast and precise non-contact velocimetry for robot applications. A technique for the precise measurement of the speed between two sliding surfaces has been developed during the research project for the realisation of an autonomous robot. The robot is devoted to the scouting of dangerous sites and to the execution of measurements in these places for the exploration of an extreme Antarctica environment (RAS project). This technique is based on the precise calculation of the common movement of a laser speckle field. This approach allows the realisation of a velocimeter suitable for use in extreme conditions. A description of the adopted methodology and the obtained results are the main topic of our work. Keywords: Speckle velocimetry, Robotics 1. INTRODUCTION The purpose of the present work is the development of a precision velocimeter for an independent robotized vehicle ("snow cat") in conditions of Antarctic region. The interest to this problem is caused by the difficulties of the precision velocimetry by standard methods in conditions of probable skid and absence of unequivocal reference points at the extensive snow or ice field. Really, it is well known that the problem of very accurate dynamic control of a dynamic system in low-medium friction conditions is not an easy task. Because of the very poor precision of the odometry signal (caused by sliding) and of the GPS data (that is at a low data rate) an additional, more reliable, data source is required. To achieve this aim, a complex theoretical and experimental work has been undertaken, whose preliminary results already look rather satisfactory. This paper continues our recent works [1-3]. The exploitation of a laser velocimetry technique could allow us to solve this problem because of the potentially very high precision and quick response. Whenever a light source is projected on a real surface, the surface profile causes interference phenomena. In case of some roughness of a real surface (unavoidable at the light wavelength dimension) the interference pattern becomes irregular and gives origin to the so called speckles, caused by the different path length among the surface different points and the detector pixels. Each surface exhibits a peculiar speckle pattern, which depends on the roughness and on the incoming light. During a slow movement, upon suitable optical conditions, the pattern is preserved and can be recognized in successive images. Owing to the little dimension of the light wavelength with respect to the surface irregularity, as already stated, the laser coherence can allow the creation of speckles also on a very flat surface like the blue ice, allowing to detect anyway the movement. Now we put the task to experimental analysis of the application in non-ideal conditions, to develop the adequate mathematical algorithms and software, and to make a conclusion about the real application. * Further author information: (Send correspondence to A.A.Aliverdiev) A.A. Aliverdiev: aliverdi@frascati.enea.it, M. Caponero: caponero@frascati.enea.it, C. Moriconi: moriconi@casaccia.enea.it. Second International Conference on Advanced Optoelectronics and Lasers, edited by Igor A. Sukhoivanov, Vasily A. Svich, Yuriy S. Shmaliy, Proc. of SPIE Vol. 79, 791J, (8) X/8/$18 doi: / SPIE Digital Library -- Subscriber Archive Copy Proc. of SPIE Vol J-1

2 . THE EXPERIMENTAL SET-UP To carry out the demonstration tests we have built an experimental breadboard, presented on the figure 3. N) Figure 1. The sketch of experimental set up. A beam generated by a He-Ne laser source is projected through a system of lenses on to a flat white surface. The light scattered by the white surface is collected, through the system of lenses, by the high-rate camera Dalsa (Model DS-41-65K955). The acquisition equipment is composed by a very fast PC frame grabber and a dual processor XEON.4 GHz PC. The described optical equipment (camera and laser) is mounted on two degrees of freedom Cartesian robot, to simulate the vehicle motion. The axes motion is achieved by means of a couple of DC brushless motors, equipped with both differential encoders and tachometers to increase the response characteristics. The robot control system is based on a VME bus controller composed of a CPU board (Motorola MVME16) for the calculations inherent to the control law and to the trajectories definition, a piggy-back module (mounted on the CPU) for the encoder reading and the low-level control of trajectories, a digital input board for the reading of the proximity switches limiting the axes excursion, and an analogue input VME board dedicated to the management of the X axis movement. Recently we have modified our experimental breadboard, making full co-lineation of the laser and camera using beam-splitter. It has given us the possibility to make our measurements for the surfaces with complex relief. But the presented in this paper data were obtained using breadboard shown on a figure THE MATHEMATICAL BASIS OF METHOD Several approaches that rely on both time and space statistics have been suggested. Differential [4] and integral [5] (with respect to time) intensity functions have been used. Our initial approach was aimed at modifying the analysis of an integrated statistics. Namely, instead of a set of averaging times, we take the average for one value of the averaging time T, but for a set of angles in the spatial-temporal plane [6-8]. The result is the transformation of the intensity function I(x,t), just like a direct Radon-transformation, but with fixed integral limits: T s p g( s, ) I( s cos( p sin(, sin( cos( ) dp. (1) Tv Proc. of SPIE Vol J-

3 s ) corresponds to the angle, s s which is a representation of the real velocity v tan( s max ). If the time is measured in the number of frames and x in number of pixels, then v 1, but we must consider this coefficient in a final calculation of the searched velocity. The parameter s here is the analogue of spatial parameter, from which we can calculate the r.m.s. spatial deviation The maximum value of the r.m.s. spatial deviation ( ( g( s, g( s, Than developing our approach, we face the problem to define not only the velocity module, but also the motion direction, to find the vector v ( v x, v y ). Considering that in case of non-zero value of the orthogonal speed, traces drawn by speckles quickly abandon the researched area, we suggest to modify the first equation, namely, to add the integration on the orthogonal direction: T T s p g x ( s, ) I x ( s cos( p sin(, sin( cos( ) dpdy, () T v T v T T s p g y ( s, ) I ( s cos( p sin(, sin( cos( ) dpdx, (3) y T v T v It is important, that the choice of the integral-limits for the orthogonal dimension is a delicate question. If they are too large, then the spot-picture may be washed out, but if they are too small, the presence of an orthogonal velocity component can disturbs the velocity-caused maximum of the function s (. The analytical solution of this problem has been proved to be not an easy task. Empirically we found that the equivalents of the orthogonal and direct sizes are optimal for our measurements. The first experiments demonstrated that a precise speed measurement without some adjustments of the standard deviation measurement is possible only in a narrow range of angles, close to the true direction of the motion. It is important, that for the calculation of velocity we need to made some primarily mathematical development of the input function I to plane the Gauss profile of the laser spot (fig. ), and some optimisations in the procedure of the maximum contrast search. X(pkcefs) Figure. The initial transformation of the input signal. The lower surface is the input signal, the higher after transformation. Moreover to neglect the influence of unsteady spatial frequencies in the initial images, we apply the following function in place of the s ( : ( g( s s, g( s,. [3] s Proc. of SPIE Vol J-3

4 The function s ( greatly depends on the parameter s : (. But a nonzero value of s, however, it enables us to cut off low spatial frequencies, and to give possibility to obtain good results even without primarily developing of the input function I, which we mention over. 4. EXPERIMENT RESULTS AND DISCUSSION We have tested our velocimeter with different kinds of surfaces, and different trajectories of motion. For the control of the precision of our method we have provided the angle-resolved velocimetry, that is the velocimetry for the set of the angles between the axe Ox and the direction of the velocity measurement. So for each angle we had the local coordinate system ( x, y, which was rotated for the angle relative coordinate system (x, y) and for which we calculated the velocity in the direction of axe Ox. In real-time operation the algorithm calculates only two orthogonal components v x and v y, but the scheme obtained in this way allow us to estimate the absolute and relative error of our calculations. Really, if the measurement of velocity is correct, we always have to have the proper sinusoid function. In the fig. 3-6, we present some results, obtained introducing non-ideal conditions and verified at different velocities. The breadboard allowed us to superimpose noise effects (like vibrations) and to modify measurement conditions (like the camera rate) in order to better estimate the behavior of the method under different conditions. Fig. 3 presents the results of measurement of the certain velocity v=1 cm/sec, assigned by the robot system. Diagram 3 presents the dependence of the maximum value of from (vertical axis) and from the angle of a turn (horizontal axis). So, diagrams 3 are in fact 3D diagrams were the value of the function is represented in terms of intensity. In the plots 3 you will find more immediately the dependence of the velocity from the angle. -, ti,, frt - \ \ 'I' / \, l Figure 3. The dependence of the maximum the dependence of the velocity from. (v=1 cm/sec). Proc. of SPIE Vol J-4

5 /,, -p " ¼, ' \, I / lou 1 lu U U 36 Figure 4. The dependence of the maximum the dependence of the velocity from. (v=5 cm/sec). Figures 4-6 present the same values, but for the different measurements with different velocities (here we present 5 cm/sec and 1 cm/sec, but we have reported the similar data from 1 up 3 cm/sec). We can see, that we have very good precision (with relative error for the front direction less than %) for these frameworks of velocities (really, more than.3 and less than 3 in relative unites). When the velocity is higher than 3 in relatives units (pixels per frames), discrete matrix became to be more significant. Nevertheless with less precision (in the frameworks 5-1 %) this method can be used up to 5-7 relatives units. When velocity is lower.3 relative precision falls down and because of discrete matrix, both because of velocity became to be non-constant for the measured time. ID 5 U ID IOU 1 I Figure 5. The dependence of the maximum the dependence of the velocity from. (v=1 cm/sec with the strong vibration). Let us compare the results, obtained with the same velocities, but with additional vibration in orthogonal direction, controlled be the computer (figures 3 and 5 for v=1 cm/sec, and figures 4 and 6 for v=5 cm/sec accordantly). We can see, that for v=1 cm/sec, we loose precision, but it stay considerable. But for v=5 cm/sec the dependence of the velocity from the angle is not proper sinusoid. The reason is a large variation of velocity for the time of 18 frames. We can Proc. of SPIE Vol J-5

6 see it in the fig. 6. Really we have not one velocity, but few velocities, the difference between each more than 1 %. In this case our method of calculation finds not their middle value, but one of them, and it is different for each l Figure 6. The dependence of the maximum the dependence of the velocity from. (v=5 cm/sec with the strong vibration). More clear this effect we can see in the fig. 7. It presents the measurement of velocity in the moment of its fast changing. In the dependents of r. m. s. from and we clearly see two sinusoids, correspondents for two different velocities. In the final velocity calculation we have or first or second velocity, but again not their middle value, that we see in the angle-resolves velocity dependents. ID V V1 V 5 U U O 6U 8U IUU 1U IO 16U 18U UU U O 6U 8U 3UU 3U 3O 36U 36U Figure 7. The dependence of the maximum the dependence of the velocity from. (for the non-stable be-component velocity, in cm/sec). To overcome this problem, we a little modify the algorithm of the velocity calculation, and make it sensitive to other large peaks of. The result of the application of modified algorithm for the fixed, and fast-variable velocities are presented in the figures 8 and 9. They demonstrate the time-dependence (in the number of frames) of the speckle filed along axis X (the vertical axis, 18 pixel total), integrated by the axis Y, and the time-dependence (in the number of frames) of the measured velocity (in the relative unites pixel/frame) the fixed and for the variable velocity accordantly. We can see, that the precision stays good (less -3 %) even in this extreme for our algorithm conditions. Proc. of SPIE Vol J-6

7 3 boo 1 O J 7 P bob 11 Figure 8. The time-dependence (in the number of frames) of the speckle filed along axis-x (the vertical axis, 18 pixel total), integrated by the axis Y, and the time-dependence (in the number of frames) of the measured velocity (in the relative unites pixel/frame) for the fixed velocity (with addition of strong vibration). Figure 9. The time-dependence (in the number of frames) of the speckle filed along axis-x (the vertical axis, 18 pixel total), integrated by the axis Y, and the time-dependence (in the number of frames) of the measured velocity (in the relative unites pixel/frame) for the variable velocity. Now we continue to work and for the modernization of our breadboard (we told about it over), both with its work with the possible non-ideal conditions. CONCLUSION The presented results give us a base to conclude about possibility to apply the considered method of precise velocimetry for the RAS. This method can be especially useful for the low friction conditions when the velocities are not too high, and from other hand other methods gives the worst results. Proc. of SPIE Vol J-7

8 ACKNOWLEDGEMENTS The authors would like to thank ENEA, the CNR-NATO program, and the Ministry of Education and Science of Russia for the program The development of the potential of Higher School which made this study possible (3454). REFERENCES 1. A. Aliverdiev, M. Caponero, C. Moriconi, "Speckle Velocimeter for a Self-Powered Vehicle", Tech. Phys., No.8, pp ,.. A. Aliverdiev, M. Caponero, C. Moriconi, "Speckle-velocimeter for robotized vehicles", in ALT' International Conference on Advanced Laser Technologies, Heinz P. Weber, Vitali I. Konov, Thomas Graf, ed., Proc. of SPIE 5147, pp , A. Aliverdiev, M. Caponero, and C. Moriconi, "Some Issues Concerning the Development of a Speckle Velocimeter", Technical Physics, Vol. 48, No. 11, 3, pp A. F. Fercher, "Velocity measurement by first-order statistics of time-differentiated laser speckles," Opt. Commun. 33, pp , A. F. Fercher and J. D. Briers, "Flow visualization by means of single-exposure speckle photography," Opt. Commun. 37, pp , A. F. Fercher, M. Peukert and E. Roth, "Visualization and measurement of retinal blood flow by means of laser speckle photography," Opt. Eng. 5, pp , J. D. Briers and S. Webster, "Quasi-real time digital version of single-exposure speckle photography for full-field monitoring of velocity or flow fields," Opt. Commun. 116, pp. 36-4, J. D. Briers, G. Richards and X. W. He, "Capillary blood flow monitoring using laser speckle contrast analysis (LASCA)," J. Biomed. Opt., 4, pp , Proc. of SPIE Vol J-8